Consider a typical hollow fibre membrane module as shown in FIG. 1. The module consists of plurality of hollow fibre membranes 5 potted at least at one end into a pot 6 having a length L. In order to calculate the flow from individual fibres the TMP (Transmembrane pressure P1-P2) is considered as acting across a total module resistance R to give a flow Q:TMP/R αQ (at constant temperature)Now in this typical model we can break the resistance down into:R=Rm+Rpotand QiαTMP/(Rm+Rpot)where Qi is the flow emerging from the top of the intact fibre, Rm is the module resistance and Rpot is the resistance across the pot.
We can assume Rm is constant—a sort of average—though it will vary down the length of the fibre.
Now taking the case where a fibre is broken at the top pot (a worst case for filtrate bypass). In this case:Rm=0and QbαTMP/Rpotwhere Qb is the flow of filtrate emerging from the top of the broken fibre.
The ratio of the flow down a broken fibre to the flow down an intact fibre is calculated as follows:
                    =                                            Q              b                        /                          Q              i                                =                    ⁢                                    (                                                R                  m                                +                                  R                  pot                                            )                        /                          R              pot                                                              =                ⁢                  1          +                                    R              m                        /                          R              pot                                          
In the normal case Rm>>Rpot—typically 20. Thus it can be seen a broken fibre allows a significant amount of feed to contaminate the filtrate and thus degrade filtration performance. Additionally, increasing the internal diameter of the fibre makes the problem massively worse as typically Rpot α L/d4, where d is the diameter of the lumen and L is the length of the pot.
Accordingly, it is desirable to reduce the flow of filtrate from a broken fibre. Take the case where we increase Rpot (for instance by increasing L or reducing d). The limit of Qb/Qi tends to 1. This is a highly desirable result. But increasing the length of the pot is undesirable in other ways—it increases the length of the module and the expense of the module and process. The other option is to reducing the internal diameter of the fibre in the pot.